What is Density functional theory: Definition and 22 Discussions

Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry.
DFT has been very popular for calculations in solid-state physics since the 1970s. However, DFT was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions. Computational costs are relatively low when compared to traditional methods, such as exchange only Hartree–Fock theory and its descendants that include electron correlation. Since, DFT has become an important tool for methods of nuclear spectroscopy such as Mössbauer spectroscopy or perturbed angular correlation, in order to understand the origin of specific electric field gradients in crystals.
Despite recent improvements, there are still difficulties in using density functional theory to properly describe: intermolecular interactions (of critical importance to understanding chemical reactions), especially van der Waals forces (dispersion); charge transfer excitations; transition states, global potential energy surfaces, dopant interactions and some strongly correlated systems; and in calculations of the band gap and ferromagnetism in semiconductors. The incomplete treatment of dispersion can adversely affect the accuracy of DFT (at least when used alone and uncorrected) in the treatment of systems which are dominated by dispersion (e.g. interacting noble gas atoms) or where dispersion competes significantly with other effects (e.g. in biomolecules). The development of new DFT methods designed to overcome this problem, by alterations to the functional or by the inclusion of additive terms, is a current research topic. Classical density functional theory uses a similar formalism to calculate properties of non-uniform classical fluids.
Despite the current popularity of these alterations or of the inclusion of additional terms, they are reported to stray away from the search for the exact functional. Further, DFT potentials obtained with adjustable parameters are no longer true DFT potentials, given that they are not functional derivatives of the exchange correlation energy with respect to the charge density. Consequently, it is not clear if the second theorem of DFT holds in such conditions.

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  1. M

    A How does DFT handle degenerate eigenvectors?

    I have a question about how DFT (density functional theory) handles degenerate states. The Hamiltonian in DFT is a functional of the electron density defined via ##n(\mathbf{r})=\sum^N_{k=1}|\psi_k(\mathbf{r})|^2##. However, say I have a pair of degenerate states. Then any linear combination of...
  2. Y

    A Learning DFT: Inhomogeneous Electron Gas (Hohenberg) Question

    I'm reading through Hohenberg's seminal paper titled: "Inhomogeneous Electron Gas" that help lay the foundation for what we know of as Density Functional Theory (DFT) by proving the existence of a universal functional that exactly matches the ground-state energy of a system with a given...
  3. Dario56

    I Potential Energy of an Electron-Nuclei Interaction in DFT

    In density functional theory (DFT), electron density is a central quantity. Because of this, we want to calculate electron - nuclei potential energy as functional on electron density. If we know how potential energy varies across space, we can calculate this functional with plugging particular...
  4. A

    I Density Functional Theory and pseudopotentials

    Hi, I have a blog oriented on computational physics: https://compphys.go.ro For many posts I have a GitHub project. Lately I started some DFT oriented ones, the latest being a DFT (with plane waves basis) project for a 'quantum dot'. Currently I started working on a project that will use the...
  5. Ben Wilson

    A Getting Started with CASTEP: Installing & Configuring for DFT Calculations

    Hi guys, I'm trying to use the CASTEP software for dft calculations. I have plenty of documentation on how to use it once it's all up and running, however I don't know how to get to that point :/ I'm not the best with linux but I've manually installed programs before through tarballs but here...
  6. August

    Density Functional Theory (DFT) textbooks

    I'm starting out on DFT right now. I'm an experimental Physics student, so I'm not very familiar with theories. Can you recommend any good textbooks or resources that I can utilize for my study?? Thanks in advance.
  7. L

    If there's any website that can upload my programming script

    Hi there, Apologize in advance if this is not the correct place to post my query. I've been googling didn't get it or maybe my input search parameter is not sufficient or irrelevant. I am recently doing my graduate in physics and my inclination towards computational physics makes me to do my...
  8. G

    Mass Given Density Function and Area

    Homework Statement A quarter disc of radius 3 cm lies in the first quadrant. The areal density is (1.2 g/cm3)x + (0.7 g/cm3)y. Determine the mass of this object. Homework Equations The Attempt at a Solution For my bounds: x: 0 to 3 y: 0 to Sqrt[3 - x^2] When I took this integral I got...
  9. M

    How big should a defected supercell be? DFT

    When studying defects using plane-wave basis density functional theory, it is necessary to ensure that the size of the supercell in which the defect is located is large enough to ensure that there is no interaction between the defect in question, and the periodically repeated defects that are a...
  10. S

    DFPT second order energy variational form

    I am referring to perturbation expansion of density functional Kohn Sham energy expression in Phys. Rev. A 52, 1096. In equation (92) the variational form of the second order energy is listed, but I cannot seem to work out the last 3 terms involving XC energy and density. Particularly, the...
  11. M

    CASTEP simulation for graphene band structure

    Homework Statement I am running CASTEP DFT software to simulate pristine graphene, and am unsuccessful in obtaining the trademark zero band gap at the k-point as reported in numerous papers to date. Any assistance would be greatly appreciated as the subject is very new but I am keen to push...
  12. A

    Density functional theory and partial charge transfer

    When density functional theory is used to simulate a molecule adsorbed on a surface, it turns out that due to their interaction, a fraction of an electron is transferred from the surface to the molecule or vice versa. These interactions are normally categorised in interactions involving...
  13. P

    Question on density functional theory

    Dear PF, I'm reading a book on DFT, and it says that only ground-state wave function is a unique functional of the ground-state density, n(r). However, if in DFT the potential, v(r), is a unique functional of n(r), then shouldn't all wave functions be functionals of n(r), because you can...
  14. V

    Using Density Functional Theory to make a Tight Binding model?

    Hi all, A professor asked me to do something, but I'm not quite sure what he means -- He asked me to use Density Functional Theory (DFT) calculations of the band structure of a certain crystalline metal and adjust the matrix elements of a Tight Binding (TB) model to make a "minimal" TB model...
  15. A

    Density Functional Theory

    I am a new user for Quantum Espresso(QE). Recently I have installed Quantum Espresso in my system. Now i am struggling to give input file in QE. How to generate input file in QE?
  16. D

    Worried about Eng Masters using Density Functional Theory and Career Flexibility

    I just finished my undergrad in Chem Eng and am very interested in energy field ( I was thinking of doing something with battery and storage systems as it is closest to my field). I was recently offered a masters in MSE for possibly working on battery materials using Density Functional Theory...
  17. E

    Density Functional Theory

    Hi,all Is there someone's research related to DFT? I'm an undergraduate trying to get into it. I hope I could get some help hear if I have any question about that! Thanks a lot,Euphemia
  18. J

    Density Functional Theory and the Local Density Approximation

    Im trying to calculate the ground state energy of Helium using a density functional theory approach combined with the local density approximation. So far I have set up universal functionals and I mainly need help with the actual algorithm the evaluation of the Hartree energy functional.
  19. S

    Start Learning Density Functional Theory: A Guide for Beginners

    Hi, I want to start reading about Density Functional Theory and get through some of its approaches. I have a vey weak back ground of solid state physics. Please guide me what is the best resource to start reading. Regards
  20. K

    Basic density functional theory

    I try to learn DFT by myself(Kohn-Sham Equations), but the concept is still not so clear for me. So far, if I start with assuming any density, and then I would be able to find V(KS) Then I use this hamiltonian and solve for a wave function. And I use this wave function to find another...
  21. G

    Density functional theory, and Kohn Sham equations

    Hi, i am looking for papers, books, etc, related with the Density functional theory, and Kohn Sham equations, i appreciate any help. Thanks. :rolleyes:
  22. R

    Is my methodology for learning density functional theory correct?

    I'm trying to learn density functional theory by myself, but I'm a bit confused as to how to use it. Is the following methodology correct (I think it'd take forever to use LaTex to write the equations, so I have a link to small webpage that already has the equations laid out and numbered)...